K Deduction, Matters of Reason, and Matters of Fact

Philosophers sometimes divide concepts into matters of reason and matters of fact (these categories have other names as well). We can unambiguously deter­mine the truths of matters of reason because they have to do with the meanings of words and their relationships in sentences.

A common form of deductive reasoning involves the syllogism, an argument having a general statement, a specific statement, and a conclusion. The general statement is the major premise; the specific statement is the minor premise. Sometimes you see this with the major premise designated “P,” the minor one “Q,” and the conclusion “R.” The syllogism says that “if P and Q are true, R must be true.” If you agree that no rocks are alive (P) and that this object is a rock (Q), then you must agree that this object is not alive (R). And you must agree, not be­cause the logic police could arrest you if you don't agree, but because you are a rational person who understands the meanings of the words and who expects meanings to apply consistently.

The syllogism is one form of a deductively valid argument. As a rule, if a true conclusion necessarily follows from true premises, then the argument is a valid deductive argument.³⁹ Mathematical truths are in this category. “Two plus two equals four” is true because the meanings of “two,” “plus,” “equals,” and “four” are defined so that this statement has to be true. In the artificial environments of mathematics and symbolic logic, so-called closed systems, you can prove the Truth of most, though not all, statements by deductive reasoning. Deductively valid statements in these systems tell you nothing about the nonmathematical, empirical world.

Another form of nonmathematical argument that is logically true is a tautology.

“Why is Fido eating that smelly cat food?”

“Because he likes it.”

“How do you know he likes it?”

“Because he's eating it.”

That's a tautology; it essentially equates eating and liking. The conclusion that Fido likes smelly cat food is based on the fact that he's eating it, together with the implicit assumption that eating it means he likes it. The tautology is logically valid though empirically meaningless; it says nothing about the real motivation for Fido's food choice. Maybe he doesn't actually like cat food of any kind—he wouldn't choose it if he had options—but now he is starving and will eat anything he can gag down.

Deductive reasoning is safe and secure and, for nearly two thousand years, from the time of Aristotle until the 1500s, philosophers thought that they could accumulate knowledge about the world through deductive reasoning alone. It might work like this: Suppose we assume that “people who earn more than $250,000 annually are rich,” and, since Pat earns more than $250,000 annually, we conclude that Pat is rich. It might appear that we have gotten some new know­ledge about Pat, but, once again, we are only working with word meanings. The argument essentially defines “rich” to mean “is earning more than $250,000 an­nually.” However, being rich in some social strata might mean earning more than $1,000,000 annually, and, in that case, Pat would merely be well-off, not rich. Eventually it became clear that, by itself, this deductive procedure was not getting anywhere. The problem was that the fundamental notions that philosophers had about the world, which they had taken to be as certain as Euclid's axioms about geometry, were actually uncertain and that deductive reasoning from them could not lead to indubitably true conclusions. So deduction could not guarantee the truth of scientific conclusions.

The question is not whether deductive reasoning alone is sufficient for making scientific progress—it is not; the question is whether deductive reasoning has a place in science or scientific reasoning, and it does. As we'll see in Chapter 2, hypotheses and predictions are connected logically; we deduce predictions from hypotheses. Before exploring that relationship, however, we need to examine the major alternative to deductive reasoning.

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